First, a conventional demodulator will be explained. FIG. 10 is a diagram showing a structure of a prior demodulator (corresponding to a multiple differential phase detector 500) disclosed in “Differential Detection Scheme for DPSK using Phase Sequence Estimation” (Institute of Electronics, Information and Communication Engineers, Technical Report, RCS98-102, January, 1993).
The conventional demodulator comprises, a multiple differential phase detector 500 for generating/outputting demodulated data from a received signal, a 1 symbol differential phase detector 510, a multiple symbol differential phase detector 520, and a Viterbi sequence estimation unit 530. A receiver (not shown) that makes use of the multiple differential phase detector 500, a Viterbi decoder is provided which decodes demodulated data using Viterbi algorithm, and generates decoded data.
The 1 symbol differential phase detector 510 comprises following components. Namely, a delay element 511 stores the received signal of 1 symbol before, and a phase comparator 512 obtains a phase difference between a current received signal and the received signal of 1 symbol before and outputs a 1 symbol differential phase detected signal. The multiple symbol differential phase detector 520 comprises following components. Namely, delay elements 521-1, . . . , 521-(N−1) store past 1 symbol differential phase detected signals, and adders 522-1, . . . , 522-(N−1) obtain a sum of 1 symbol detected phases output from the delay elements 521-1, . . . , 521-(N−1).
Operation of a transmitter will be explained here in simple manner. In the transmitter, transmitted data ai∈{−1,1} are subject to convolutional coding, and convolutional-coded data di are output. For example, when the coding rate of the convolutional code is considered be 1/2, the convolutional-coded data can be represented by [di=(Pi,Qi):Pi,Qi∈{−1,1}]. The output convolutional-coded data (Pi,Qi) are converted into transmission differential phase Δθi=F(Pi,Qi). For example, when differential QPSK (Quaternary Phase Shift Keying) modulation is adopted as the modulation method, the conversion rule F can be represented as shown in FIG. 11.
Then, transmission signal phase of 1 symbol before θi−1 and the converted transmission differential phase Δθi are added according to the following recurrence equation (1) to generate the current transmission signal phase θi, and this phase is then output.θi=θi-1+Δθi  (1)
Further, the phase is modulated according to the output transmission signal phase θi, and a signal whose phase has been modulated is output as a transmission signal.
Operation of the receiver having the multiple differential phase detector 500 shown in FIG. 10 will now be explained. Received signal is input into the delay element 511 and the phase comparator 512 of the 1 symbol differential phase detector 510. The delay element 511 holds the received signal of 1 symbol before and inputs it into the phase comparator 512. The phase comparator 512 compares a phase of the current received signal and a phase of the received signal of 1 symbol before and obtains a phase difference of the signals and output a 1 symbol differential phase detected signal as the result of comparison.
When the phase of the received signal at time i is taken as φi, the 1 symbol differential phase detection signal Δ φ(1)i output from the phase comparator 512 is represented by the following formula (2).Δψ(1)i=ψi−ψi−1  (2)
That is, the 1 symbol differential phase detected signal Δφ(1)i represents a difference in phase of the received signal for 1 symbol cycle, and when noise and fading do not occur, the value is equal to the transmitted differential phase Δ θi. Since the value of the transmitted differential phase Δθi is determined by transmitted data ai as mentioned above, transmitted data can be estimated by using the value of the 1 symbol differential phase detected signal Δφ(1)i.
The 1 symbol differential phase detected signal Δφ(1)i output from the phase comparator 512 is input into the delay element 521-1 of the multiple symbol differential phase detector 520. The delay element 521-1 gives a delayof 1 symbol cycle of the received signal to the signal Δφ(1)i. The output of the delay element 521-1 is input into the adder 522-1. The 1 symbol differential phase detected signal Δφ(1)i output from the phase comparator 512 is also input into the adder 522-1. That is, the adder 522-1 adds the 1 symbol differential phase detected signal Δφ(1)i and the output Δφ(1)i−1 of the delay element 522-1.
Therefore, when the output (sum of a changing amount of delay) of the adder 522-1 is taken to be Δφ(2)i, then the formula (3) holds.Δψ(2)i=Δψ(1)i+Δψ(1)i−1=ψi−ψi−1−ψi−2=ψi−ψi−2  (3)
That is, the output Δφ(2)i of the adder 522-1 becomes a 2 symbol differential phase detected signal representing a difference amount of phase for 2 symbol periods of the received signal.
Total (N−1) units of delay elements 521-1, 521-2, . . . , 521-(N−1) are connected in parallel. The m-th (m=2, . . . , N−1) delay element delays the output of the (m−1)-th delay element by an amount which is equal to the 1 symbol period of the received signal before outputting. Therefore, the output of the m-th (m−1, 2, . . . , N−1) delay element will be Δφ(1)i−m.
Further, total (N−1) units of adders 522-1, 522-2, . . . , 522-(N−1) are connected in file. The output of the (m−1)th adder is input into the m-th (m−2, . . . , N−1) adder. Moreover, the outputs of the delay elements 521-1, 521-2, . . . 521-(N−1) are also input into the adders 522-1, 522-2, . . . , 522-(N−1). That is, the m-th (m−2, . . . , N−1) adder adds the output of the (m−1)th adder and the output of the m-th delay element and outputs the result.
Therefore, when the output of the m-th (m−2, . . . , N−1) adder at time i is taken to be Δφ(m+1)i, then the formula (4) holds.Δψ(m+1)i=Δψ(m)i+Δψ(1)i−m=Δψ(m)i+(ψi−m−ψi−m−1)  (4)
Formula (4) is a recurrence formula about Δφ(m)i. When this formula is solved, the formula (5) is obtained.
                                                                        Δψ                                                      (                                          m                      +                      1                                        )                                    ⁢                  i                                            =                                                Δψ                                                            (                      2                      )                                        ⁢                    i                                                  +                                                      ∑                                          j                      =                      1                                        m                                    ⁢                                      (                                                                  ψ                                                  i                          -                          j                                                                    -                                              ψ                                                  i                          -                          j                          -                          1                                                                                      )                                                                                                                          =                                                Δψ                                                            (                      2                      )                                        ⁢                    i                                                  +                                  ψ                                      i                    -                    2                                                  -                                  ψ                                      i                    -                    m                    -                    1                                                                                                                          =                                                (                                                            ψ                      i                                        -                                          ψ                                              i                        -                        2                                                                              )                                +                                  ψ                                      i                    -                    2                                                  -                                  ψ                                      i                    -                    m                    -                    1                                                                                                                          =                                                ψ                  i                                -                                  ψ                                      i                    -                                          (                                              m                        +                        1                                            )                                                                                                                              (        5        )            
That is, the output value Δφ(m+1)i of the m-th (m−2, . . . , N−1) adder becomes a (m+1) symbol differential phase detected signal representing a difference of phase for (m+1) symbol period of the received signal. Thus, 2, 3, . . . , N symbol differential phase detected signals are output from the total of (N−1) adders 522-1, 522-2, . . . , 522-(N−1).
The multiple symbol differential phase detector 520 combines the total of (N−1) differential phase detection signals Δφ(2)i, . . . , Δφ(N)i and the 1 symbol differential phase detected signal Δφ(1)i output from the phase comparator 512, and generates multiple differential phase detected signals Δφi=(Δφ(1)i, Δφ(2)i, . . . , Δφ(N)i). The number N of the multiple differential phase detected signals is referred to as a maximum delay symbol number.
The Viterbi sequence estimation unit 530 estimates a transmitted differential phase sequence according to known Viterbi algorithm using a trellis diagram representing state transitions composed of a combination of (N−1) transmission differential phase signal points. Precisely, for example, when M-PSK modulation is used on the transmission side, replicas of 1, 2, . . . , N symbol differential phase detected signals are assumed for MN state transitions. Branch metric is calculated for all the state transitions on the trellis diagram based on the multiple differential phase detected signals Δφi=(Δφ(1)i, Δφ(2)i, . . . , Δφ(N)i).
Thereafter, the Viterbi sequence estimation unit 530 executes addition and comparison (ACS: Add-Compare-Select) based on the Viterbi algorithm, and selects survival path metrics for each state, and stores the selected paths into an internal path memory (not shown) and updates the path metrics. Hard decision is made for a bit corresponding to a path where the path metric finally becomes minimum/maximum, and demodulated data as the hard decision result are output from the differential phase detector 500.
A Viterbi decoder (not shown) on the receiver side decodes the demodulated data of the hard decision using the known Viterbi decoding method, and outputs the decoded data. Here, as the Viterbi decoding method, for example “Coding Theory” written by Imai Hideki, the Institute of Electronics, Information and Communication Engineers (1990) (in Japanese) may be used.
The conventional demodulator, namely, the multi differential phase detector outputs demodulated data obtained by the hard decision, and the Viterbi decoder of the receiver reproduces original transmitted data using the hard decided demodulated data.
However, in the conventional demodulator, since the multiple differential phase detector outputs the demodulated data according to the hard decision, namely, since an input into the Viterbi decoder is the hard decision value, a correcting capability of convolutional codes cannot be drawn out sufficiently as compared to the case where the input into the Viterbi decoder is a soft decision value.